For Warner Bros. and other U.S. studios, the international TV-licensing bazaar has never been more lucrative.

One evening in May, Warner Bros. executive Jeffrey Schlesinger hosted a lavish dinner in the garden of his home in the Hollywood hills. He invited stars and producers from the studio’s coming shows like the Batman prequel “Gotham” and crime drama “Forever.”

But the real VIPs were executives from foreign TV channels, among the 1,400 who were visiting Los Angeles that week to shop for the latest American fare. Over flat-iron steak and...